The proposed research is motivated by problems arising in the design and analysis of complex cancer clinical trials. A general goal is to accommodate clinical settings, data structures and scientific aims that are more complex than those addressed by designs in the conventional phase I phase II phase III paradigm. The proposed research deals with trials having sequential, outcome-adaptive decisions, including selecting what treatment, dose or schedule to give the next patient, deciding whether the trial should be stopped early, deciding whether accrual should be stopped for particular patient subgroups, and what final conclusions may be drawn about treatment effects. At each interim analysis during trial conduct, a Bayesian model is fit to the current data and posterior-based decision criteria are computed and applied. Each design's operating characteristics are evaluated by computer simulation under a set of scenarios, where a scenario is characterized by a fixed parameter vector of the assumed probability model, or under alternative probability distributions to study robustness. The scenarios are chosen to represent a suitably wide range of clinically meaningful cases. Operating characteristics include trial duration, number of patients assigned to each treatment or dose, and probabilities of possible decisions and conclusions. These evaluations are used to calibrate design parameters to ensure that the design has scientifically and ethically desirable properties. The proposed projects encompass a variety of clinical settings, including dose-finding trials, phase II-III trials, two- arm phase III trials with multiple outcomes, and any Bayesian setting where an informative prior is elicited. Models, methods, and computational algorithms will be developed for each of the following: (1) Choosing the optimal dose pair of a chemotherapeutic agent and a biologic agent used in combination. Patient outcome is a trinary vector of ordinal variables accounting for two types of toxicity, one associated with each agent, and treatment efficacy. Based on elicited numerical utilities of the possible patient outcomes, a dose pair is chosen for each successive patient cohort to maximize the current posterior mean utility. (2) Comparing multiple experimental treatments to standard therapy based on toxicity and progression-free-survival (PFS) time. The probability of a two-dimensional region based on elicited joint toxicity and PFS target probabilities will be used as the basis for treatment selection and confirmatory comparison, allowing the probability of toxicity and the PFS time distribution each to vary with patient covariates, while controlling overall generalized power and type I error. (3) Comparing treatments in a two-arm trial based on the trade-off between two outcomes such as, for example, quality of life and survival time. A general geometric method is proposed in which decisions are based on posterior probabilities of four sets that parition a two-dimensional parameter space. (4) Using nonlinear regression to estimate prior hyperparameters from elicited information. The goal is to provide a general, practical method for establishing priors in a Bayesian analysis based on information elicited from area experts in settings where the number of pieces of elicited information is much larger than the number of hyperparameters characterizing the prior. PUBLIC HEALTH RELEVANCE: The proposed research will provide more efficient and more ethically desirable designs for complex cancer clinical trials by making formal use of historical data, using individualized, patient-specific rules for treatment assignment and early stopping, and combining successive phases of treatment evaluation. The improved efficiencies will accelerate clinical evaluation and increase the likelihood that new treatments providing a clinical improvement over standard therapies will be detected while unpromising or unsafe treatments will be dropped.